Some integrated circuits contain vertical bipolar transistors, along with n-channel metal oxide semiconductor (NMOS) transistors and p-channel metal oxide semiconductor (PMOS) transistors. The vertical bipolar transistors used in circuits such as bandgap reference circuits, require high gain, for example greater than 5, and low noise, for example a signal-to-noise ratio greater than 70 decibels (dB), at collector currents of 100 picoamperes (pA) to 100 microamperes (pA). Vertical bipolar transistors in such integrated circuits are particularly susceptible to burst noise, also referred to as random telegraph signal (RTS) noise and popcorn noise. Moreover, it is desirable for the vertical bipolar transistors to occupy as little space as possible to reduce the cost of the integrated circuit. Simultaneously attaining desired levels of gain, noise and size has been problematic.